MySQL PHPMyAdmin Autocommit Off

Of the three, I prefer repair!

Looks like your phpMyAdmin was installed by the package manager, so the first thing to try is reconfiguring it. sudo dpkg-reconfigure phpmyadmin should accomplish that. Hopefully that will fix the error message you got that "phpmyadmin is broken or not fully installed" -- or if not, at least provide you with a more helpful message.

You may have other broken packages or missing dependencies, which you can try to fix with sudo aptitude -f. That will attempt to fix any broken packages.

I'm not really sure about your terminal error message. It appears that the /bin/ directory (which contains many of your system commands like ls, kill, mkdir, and many more), isn't in the list of directories used when looking for a command (the "path"). I'm hopeful that the aptitude -f will fix this too, because otherwise something really strange (and unrelated) happened to your bash configuration file.

Note that, while these are reasonably safe commands, I'm not responsible if your system explodes.

Munin's formula for "device utilization" is (milliseconds spent doing I/O)/second, which assumes you can't do any I/O in parallel, so I'm not sure that this is a meaningful metric. However, you do clearly have a genuine performance issue here since replication can't stay caught up.

Is there a significant difference in the I/O subsystems between the servers?

The way I would approach this is to compare the I/O subsystems and then if there isn't a glaring difference in architecture, run some I/O benchmarking at a quiet time with a tool like bonnie++ or fio to narrow down the difference in performance.

Note that the slave likely has an equal write workload to the master because it has replay all the writes, plus it may have a considerable read workload (for reading any parts of the database that have to be updated) and might be less efficient for reads than the master because it has less RAM for caching. In this situation I would not necessarily expect the slave to be able to catch up because it's entirely possible for the master to generate work at a rate faster than the slave can consume it.